Vertex-degree-based topological indices of arbitrary sets of hexagons in the regular hexagonal grid

Abstract

Vertex-degree-based indices have been widely used for describing and predicting physical, chemical and biological properties of molecules. They are expressed through the numbers mi,j of the edges connecting the vertices of degrees i and j. We generalize some known formulae for mi,j from graphs defined by simply connected sets of hexagons to those defined by sets of arbitrary topology in the regular hexagonal grid. We compute the most commonly used indices for three families of graphs in this grid.